Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C8×ΓL(1,𝔽25) |
| Fitting | C3×C82 ⋊ C2 |
| Sylow | C3 ⋊ C8×M16 |
224 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(12,13,14,17,15,16,18,19);(2,3)(13,16)(17,19);(4,5,6,8,7,9,10,11)144 conjugacy classes — view the full character table.
| maximal subgroup of | C16×ΓL(1,𝔽25), #10704200, #10704203, … |
| maximal normal subgroup of | C16×ΓL(1,𝔽25), #10704200, #10704203, … |
| maximal quotient of | C8×#815, #10684567, #10685611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 622);